Actual source code: ex5f90.F
1: ! "$Id: ex5f90.F,v 1.44 2001/09/11 18:47:20 bsmith Exp $";
2: !
3: ! Description: Solves a nonlinear system in parallel with SNES.
4: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
5: ! domain, using distributed arrays (DAs) to partition the parallel grid.
6: ! The command line options include:
7: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
8: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
9: !
10: !/*T
11: ! Concepts: SNES^parallel Bratu example
12: ! Concepts: DA^using distributed arrays;
13: ! Processors: n
14: !T*/
15: !
16: ! --------------------------------------------------------------------------
17: !
18: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
19: ! the partial differential equation
20: !
21: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
22: !
23: ! with boundary conditions
24: !
25: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
26: !
27: ! A finite difference approximation with the usual 5-point stencil
28: ! is used to discretize the boundary value problem to obtain a nonlinear
29: ! system of equations.
30: !
31: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
32: !
33: ! --------------------------------------------------------------------------
34: ! The following define must be used before including any PETSc include files
35: ! into a module or interface. This is because they can't handle declarations
36: ! in them
37: !
39: module f90module
40: type userctx
41: #define PETSC_AVOID_DECLARATIONS
42: #include include/finclude/petsc.h
43: #include include/finclude/petscvec.h
44: #include include/finclude/petscda.h
45: #undef PETSC_AVOID_DECLARATIONS
46: DA da
47: integer xs,xe,xm,gxs,gxe,gxm
48: integer ys,ye,ym,gys,gye,gym
49: integer mx,my,rank
50: double precision lambda
51: end type userctx
52: contains
53: ! ---------------------------------------------------------------------
54: !
55: ! FormFunction - Evaluates nonlinear function, F(x).
56: !
57: ! Input Parameters:
58: ! snes - the SNES context
59: ! X - input vector
60: ! dummy - optional user-defined context, as set by SNESSetFunction()
61: ! (not used here)
62: !
63: ! Output Parameter:
64: ! F - function vector
65: !
66: ! Notes:
67: ! This routine serves as a wrapper for the lower-level routine
68: ! "FormFunctionLocal", where the actual computations are
69: ! done using the standard Fortran style of treating the local
70: ! vector data as a multidimensional array over the local mesh.
71: ! This routine merely handles ghost point scatters and accesses
72: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
73: !
74: subroutine FormFunction(snes,X,F,user,ierr)
75: implicit none
77: #include include/finclude/petsc.h
78: #include include/finclude/petscvec.h
79: #include include/finclude/petscda.h
80: #include include/finclude/petscis.h
81: #include include/finclude/petscmat.h
82: #include include/finclude/petscksp.h
83: #include include/finclude/petscpc.h
84: #include include/finclude/petscsles.h
85: #include include/finclude/petscsnes.h
87: #include "include/finclude/petscvec.h90"
90: ! Input/output variables:
91: SNES snes
92: Vec X,F
93: integer ierr
94: type (userctx) user
96: ! Declarations for use with local arrays:
97: PetscScalar,pointer :: lx_v(:),lf_v(:)
98: Vec localX
100: ! Scatter ghost points to local vector, using the 2-step process
101: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
102: ! By placing code between these two statements, computations can
103: ! be done while messages are in transition.
105: call DAGetLocalVector(user%da,localX,ierr)
106: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
107: & localX,ierr)
108: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
110: ! Get a pointer to vector data.
111: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
112: ! the data array. Otherwise, the routine is implementation dependent.
113: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
114: ! the array.
115: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
116: ! and is useable from Fortran-90 Only.
118: call VecGetArrayF90(localX,lx_v,ierr)
119: call VecGetArrayF90(F,lf_v,ierr)
121: ! Compute function over the locally owned part of the grid
123: call FormFunctionLocal(lx_v,lf_v,user,ierr)
125: ! Restore vectors
127: call VecRestoreArrayF90(localX,lx_v,ierr)
128: call VecRestoreArrayF90(F,lf_v,ierr)
130: ! Insert values into global vector
132: call DARestoreLocalVector(user%da,localX,ierr)
133: call PetscLogFlops(11*user%ym*user%xm,ierr)
135: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
136: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
138: return
139: end subroutine formfunction
140: end module f90module
144: program main
145: use f90module
146: implicit none
147: !
148: !
149: #include include/finclude/petsc.h
150: #include include/finclude/petscvec.h
151: #include include/finclude/petscda.h
152: #include include/finclude/petscis.h
153: #include include/finclude/petscmat.h
154: #include include/finclude/petscksp.h
155: #include include/finclude/petscpc.h
156: #include include/finclude/petscsles.h
157: #include include/finclude/petscsnes.h
158: #include "include/finclude/petscvec.h90"
159: #include "include/finclude/petscda.h90"
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: ! Variable declarations
163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: !
165: ! Variables:
166: ! snes - nonlinear solver
167: ! x, r - solution, residual vectors
168: ! J - Jacobian matrix
169: ! its - iterations for convergence
170: ! Nx, Ny - number of preocessors in x- and y- directions
171: ! matrix_free - flag - 1 indicates matrix-free version
172: !
173: !
174: SNES snes
175: Vec x,r
176: Mat J
177: integer its,matrix_free,flg,ierr
178: double precision lambda_max,lambda_min
179: type (userctx) user
181: ! Note: Any user-defined Fortran routines (such as FormJacobian)
182: ! MUST be declared as external.
184: external FormInitialGuess,FormJacobian
186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: ! Initialize program
188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
191: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
193: ! Initialize problem parameters
195: lambda_max = 6.81
196: lambda_min = 0.0
197: user%lambda = 6.0
198: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
199: & user%lambda,flg,ierr)
200: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
201: & then
202: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
203: SETERRQ(1,' ',ierr)
204: endif
207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: ! Create nonlinear solver context
209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
213: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: ! Create vector data structures; set function evaluation routine
215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: ! Create distributed array (DA) to manage parallel grid and vectors
219: ! This really needs only the star-type stencil, but we use the box
220: ! stencil temporarily.
221: call DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX, &
222: & -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1, &
223: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
224: call DAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
225: & PETSC_NULL_INTEGER, &
226: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
227: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
228: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
229: & PETSC_NULL_INTEGER,ierr)
230:
231: !
232: ! Visualize the distribution of the array across the processors
233: !
234: ! call DAView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
236: ! Extract global and local vectors from DA; then duplicate for remaining
237: ! vectors that are the same types
239: call DACreateGlobalVector(user%da,x,ierr)
240: call VecDuplicate(x,r,ierr)
242: ! Get local grid boundaries (for 2-dimensional DA)
244: call DAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
245: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
246: call DAGetGhostCorners(user%da,user%gxs,user%gys, &
247: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
248: & PETSC_NULL_INTEGER,ierr)
250: ! Here we shift the starting indices up by one so that we can easily
251: ! use the Fortran convention of 1-based indices (rather 0-based indices).
253: user%xs = user%xs+1
254: user%ys = user%ys+1
255: user%gxs = user%gxs+1
256: user%gys = user%gys+1
258: user%ye = user%ys+user%ym-1
259: user%xe = user%xs+user%xm-1
260: user%gye = user%gys+user%gym-1
261: user%gxe = user%gxs+user%gxm-1
263: ! Set function evaluation routine and vector
265: call SNESSetFunction(snes,r,FormFunction,user,ierr)
267: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
268: ! Create matrix data structure; set Jacobian evaluation routine
269: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
271: ! Set Jacobian matrix data structure and default Jacobian evaluation
272: ! routine. User can override with:
273: ! -snes_fd : default finite differencing approximation of Jacobian
274: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
275: ! (unless user explicitly sets preconditioner)
276: ! -snes_mf_operator : form preconditioning matrix as set by the user,
277: ! but use matrix-free approx for Jacobian-vector
278: ! products within Newton-Krylov method
279: !
280: ! Note: For the parallel case, vectors and matrices MUST be partitioned
281: ! accordingly. When using distributed arrays (DAs) to create vectors,
282: ! the DAs determine the problem partitioning. We must explicitly
283: ! specify the local matrix dimensions upon its creation for compatibility
284: ! with the vector distribution. Thus, the generic MatCreate() routine
285: ! is NOT sufficient when working with distributed arrays.
286: !
287: ! Note: Here we only approximately preallocate storage space for the
288: ! Jacobian. See the users manual for a discussion of better techniques
289: ! for preallocating matrix memory.
291: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
292: & matrix_free,ierr)
293: if (matrix_free .eq. 0) then
294: call DAGetMatrix(user%da,MATMPIAIJ,J,ierr)
295: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
296: endif
298: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
299: ! Customize nonlinear solver; set runtime options
300: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
304: call SNESSetFromOptions(snes,ierr)
306: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: ! Evaluate initial guess; then solve nonlinear system.
308: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
310: ! Note: The user should initialize the vector, x, with the initial guess
311: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
312: ! to employ an initial guess of zero, the user should explicitly set
313: ! this vector to zero by calling VecSet().
315: call FormInitialGuess(user,x,ierr)
316: call SNESSolve(snes,x,its,ierr)
317: if (user%rank .eq. 0) then
318: write(6,100) its
319: endif
320: 100 format('Number of Newton iterations = ',i5)
322: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
323: ! Free work space. All PETSc objects should be destroyed when they
324: ! are no longer needed.
325: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
327: if (matrix_free .eq. 0) call MatDestroy(J,ierr)
328: call VecDestroy(x,ierr)
329: call VecDestroy(r,ierr)
330: call SNESDestroy(snes,ierr)
331: call DADestroy(user%da,ierr)
332: call PetscFinalize(ierr)
333: end
335: ! ---------------------------------------------------------------------
336: !
337: ! FormInitialGuess - Forms initial approximation.
338: !
339: ! Input Parameters:
340: ! X - vector
341: !
342: ! Output Parameter:
343: ! X - vector
344: !
345: ! Notes:
346: ! This routine serves as a wrapper for the lower-level routine
347: ! "InitialGuessLocal", where the actual computations are
348: ! done using the standard Fortran style of treating the local
349: ! vector data as a multidimensional array over the local mesh.
350: ! This routine merely handles ghost point scatters and accesses
351: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
352: !
353: subroutine FormInitialGuess(user,X,ierr)
354: use f90module
355: implicit none
357: #include "include/finclude/petscvec.h90"
358: #include include/finclude/petsc.h
359: #include include/finclude/petscvec.h
360: #include include/finclude/petscda.h
361: #include include/finclude/petscis.h
362: #include include/finclude/petscmat.h
363: #include include/finclude/petscksp.h
364: #include include/finclude/petscpc.h
365: #include include/finclude/petscsles.h
366: #include include/finclude/petscsnes.h
368: ! Input/output variables:
369: type (userctx) user
370: Vec X
371: integer ierr
372:
373: ! Declarations for use with local arrays:
374: PetscScalar,pointer :: lx_v(:)
375: Vec localX
377: 0
379: ! Get a pointer to vector data.
380: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
381: ! the data array. Otherwise, the routine is implementation dependent.
382: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
383: ! the array.
384: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
385: ! and is useable from Fortran-90 Only.
387: call DAGetLocalVector(user%da,localX,ierr)
388: call VecGetArrayF90(localX,lx_v,ierr)
390: ! Compute initial guess over the locally owned part of the grid
392: call InitialGuessLocal(user,lx_v,ierr)
394: ! Restore vector
396: call VecRestoreArrayF90(localX,lx_v,ierr)
398: ! Insert values into global vector
400: call DALocalToGlobal(user%da,localX,INSERT_VALUES,X,ierr)
401: call DARestoreLocalVector(user%da,localX,ierr)
403: return
404: end
406: ! ---------------------------------------------------------------------
407: !
408: ! InitialGuessLocal - Computes initial approximation, called by
409: ! the higher level routine FormInitialGuess().
410: !
411: ! Input Parameter:
412: ! x - local vector data
413: !
414: ! Output Parameters:
415: ! x - local vector data
416: ! ierr - error code
417: !
418: ! Notes:
419: ! This routine uses standard Fortran-style computations over a 2-dim array.
420: !
421: subroutine InitialGuessLocal(user,x,ierr)
422: use f90module
423: implicit none
425: #include include/finclude/petsc.h
426: #include include/finclude/petscvec.h
427: #include include/finclude/petscda.h
428: #include include/finclude/petscis.h
429: #include include/finclude/petscmat.h
430: #include include/finclude/petscksp.h
431: #include include/finclude/petscpc.h
432: #include include/finclude/petscsles.h
433: #include include/finclude/petscsnes.h
435: ! Input/output variables:
436: type (userctx) user
437: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
438: integer ierr
440: ! Local variables:
441: integer i,j,hxdhy,hydhx
442: PetscScalar temp1,temp,hx,hy,sc,one
444: ! Set parameters
446: ierr = 0
447: one = 1.0
448: hx = one/(dble(user%mx-1))
449: hy = one/(dble(user%my-1))
450: sc = hx*hy*user%lambda
451: hxdhy = hx/hy
452: hydhx = hy/hx
453: temp1 = user%lambda/(user%lambda + one)
455: do 20 j=user%ys,user%ye
456: temp = dble(min(j-1,user%my-j))*hy
457: do 10 i=user%xs,user%xe
458: if (i .eq. 1 .or. j .eq. 1 &
459: & .or. i .eq. user%mx .or. j .eq. user%my) then
460: x(i,j) = 0.0
461: else
462: x(i,j) = temp1 * &
463: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
464: endif
465: 10 continue
466: 20 continue
468: return
469: end
471: ! ---------------------------------------------------------------------
472: !
473: ! FormFunctionLocal - Computes nonlinear function, called by
474: ! the higher level routine FormFunction().
475: !
476: ! Input Parameter:
477: ! x - local vector data
478: !
479: ! Output Parameters:
480: ! f - local vector data, f(x)
481: ! ierr - error code
482: !
483: ! Notes:
484: ! This routine uses standard Fortran-style computations over a 2-dim array.
485: !
486: subroutine FormFunctionLocal(x,f,user,ierr)
487: use f90module
489: implicit none
491: ! Input/output variables:
492: type (userctx) user
493: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
494: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
495: integer ierr
497: ! Local variables:
498: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
499: PetscScalar u,uxx,uyy
500: integer i,j
502: one = 1.0
503: two = 2.0
504: hx = one/dble(user%mx-1)
505: hy = one/dble(user%my-1)
506: sc = hx*hy*user%lambda
507: hxdhy = hx/hy
508: hydhx = hy/hx
510: ! Compute function over the locally owned part of the grid
512: do 20 j=user%ys,user%ye
513: do 10 i=user%xs,user%xe
514: if (i .eq. 1 .or. j .eq. 1 &
515: & .or. i .eq. user%mx .or. j .eq. user%my) then
516: f(i,j) = x(i,j)
517: else
518: u = x(i,j)
519: uxx = hydhx * (two*u &
520: & - x(i-1,j) - x(i+1,j))
521: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
522: f(i,j) = uxx + uyy - sc*exp(u)
523: endif
524: 10 continue
525: 20 continue
527: return
528: end
530: ! ---------------------------------------------------------------------
531: !
532: ! FormJacobian - Evaluates Jacobian matrix.
533: !
534: ! Input Parameters:
535: ! snes - the SNES context
536: ! x - input vector
537: ! dummy - optional user-defined context, as set by SNESSetJacobian()
538: ! (not used here)
539: !
540: ! Output Parameters:
541: ! jac - Jacobian matrix
542: ! jac_prec - optionally different preconditioning matrix (not used here)
543: ! flag - flag indicating matrix structure
544: !
545: ! Notes:
546: ! This routine serves as a wrapper for the lower-level routine
547: ! "FormJacobianLocal", where the actual computations are
548: ! done using the standard Fortran style of treating the local
549: ! vector data as a multidimensional array over the local mesh.
550: ! This routine merely accesses the local vector data via
551: ! VecGetArrayF90() and VecRestoreArrayF90().
552: !
553: ! Notes:
554: ! Due to grid point reordering with DAs, we must always work
555: ! with the local grid points, and then transform them to the new
556: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
557: ! We cannot work directly with the global numbers for the original
558: ! uniprocessor grid!
559: !
560: ! Two methods are available for imposing this transformation
561: ! when setting matrix entries:
562: ! (A) MatSetValuesLocal(), using the local ordering (including
563: ! ghost points!)
564: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
565: ! - Associate this map with the matrix by calling
566: ! MatSetLocalToGlobalMapping() once
567: ! - Set matrix entries using the local ordering
568: ! by calling MatSetValuesLocal()
569: ! (B) MatSetValues(), using the global ordering
570: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
571: ! - Then apply this map explicitly yourself
572: ! - Set matrix entries using the global ordering by calling
573: ! MatSetValues()
574: ! Option (A) seems cleaner/easier in many cases, and is the procedure
575: ! used in this example.
576: !
577: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
578: use f90module
579: implicit none
581: #include include/finclude/petsc.h
582: #include include/finclude/petscvec.h
583: #include include/finclude/petscda.h
584: #include include/finclude/petscis.h
585: #include include/finclude/petscmat.h
586: #include include/finclude/petscksp.h
587: #include include/finclude/petscpc.h
588: #include include/finclude/petscsles.h
589: #include include/finclude/petscsnes.h
591: #include "include/finclude/petscvec.h90"
593: ! Input/output variables:
594: SNES snes
595: Vec X
596: Mat jac,jac_prec
597: MatStructure flag
598: type(userctx) user
599: integer ierr
601: ! Declarations for use with local arrays:
602: PetscScalar,pointer :: lx_v(:)
603: Vec localX
605: ! Scatter ghost points to local vector, using the 2-step process
606: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd()
607: ! Computations can be done while messages are in transition,
608: ! by placing code between these two statements.
610: call DAGetLocalVector(user%da,localX,ierr)
611: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
612: & ierr)
613: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
615: ! Get a pointer to vector data
617: call VecGetArrayF90(localX,lx_v,ierr)
619: ! Compute entries for the locally owned part of the Jacobian.
621: call FormJacobianLocal(lx_v,jac,jac_prec,user,ierr)
623: ! Assemble matrix, using the 2-step process:
624: ! MatAssemblyBegin(), MatAssemblyEnd()
625: ! Computations can be done while messages are in transition,
626: ! by placing code between these two statements.
628: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
629: call VecRestoreArrayF90(localX,lx_v,ierr)
630: call DARestoreLocalVector(user%da,localX,ierr)
631: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
633: ! Set flag to indicate that the Jacobian matrix retains an identical
634: ! nonzero structure throughout all nonlinear iterations (although the
635: ! values of the entries change). Thus, we can save some work in setting
636: ! up the preconditioner (e.g., no need to redo symbolic factorization for
637: ! ILU/ICC preconditioners).
638: ! - If the nonzero structure of the matrix is different during
639: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
640: ! must be used instead. If you are unsure whether the matrix
641: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
642: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
643: ! believes your assertion and does not check the structure
644: ! of the matrix. If you erroneously claim that the structure
645: ! is the same when it actually is not, the new preconditioner
646: ! will not function correctly. Thus, use this optimization
647: ! feature with caution!
649: flag = SAME_NONZERO_PATTERN
651: ! Tell the matrix we will never add a new nonzero location to the
652: ! matrix. If we do it will generate an error.
654: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,ierr)
656: return
657: end
659: ! ---------------------------------------------------------------------
660: !
661: ! FormJacobianLocal - Computes Jacobian matrix, called by
662: ! the higher level routine FormJacobian().
663: !
664: ! Input Parameters:
665: ! x - local vector data
666: !
667: ! Output Parameters:
668: ! jac - Jacobian matrix
669: ! jac_prec - optionally different preconditioning matrix (not used here)
670: ! ierr - error code
671: !
672: ! Notes:
673: ! This routine uses standard Fortran-style computations over a 2-dim array.
674: !
675: ! Notes:
676: ! Due to grid point reordering with DAs, we must always work
677: ! with the local grid points, and then transform them to the new
678: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
679: ! We cannot work directly with the global numbers for the original
680: ! uniprocessor grid!
681: !
682: ! Two methods are available for imposing this transformation
683: ! when setting matrix entries:
684: ! (A) MatSetValuesLocal(), using the local ordering (including
685: ! ghost points!)
686: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
687: ! - Associate this map with the matrix by calling
688: ! MatSetLocalToGlobalMapping() once
689: ! - Set matrix entries using the local ordering
690: ! by calling MatSetValuesLocal()
691: ! (B) MatSetValues(), using the global ordering
692: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
693: ! - Then apply this map explicitly yourself
694: ! - Set matrix entries using the global ordering by calling
695: ! MatSetValues()
696: ! Option (A) seems cleaner/easier in many cases, and is the procedure
697: ! used in this example.
698: !
699: subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
700: use f90module
701: implicit none
703: #include include/finclude/petsc.h
704: #include include/finclude/petscvec.h
705: #include include/finclude/petscda.h
706: #include include/finclude/petscis.h
707: #include include/finclude/petscmat.h
708: #include include/finclude/petscksp.h
709: #include include/finclude/petscpc.h
710: #include include/finclude/petscsles.h
711: #include include/finclude/petscsnes.h
713: ! Input/output variables:
714: type (userctx) user
715: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
716: Mat jac,jac_prec
717: integer ierr
719: ! Local variables:
720: integer row,col(5),i,j
721: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc,v(5)
723: ! Set parameters
725: one = 1.0
726: two = 2.0
727: hx = one/dble(user%mx-1)
728: hy = one/dble(user%my-1)
729: sc = hx*hy
730: hxdhy = hx/hy
731: hydhx = hy/hx
733: ! Compute entries for the locally owned part of the Jacobian.
734: ! - Currently, all PETSc parallel matrix formats are partitioned by
735: ! contiguous chunks of rows across the processors.
736: ! - Each processor needs to insert only elements that it owns
737: ! locally (but any non-local elements will be sent to the
738: ! appropriate processor during matrix assembly).
739: ! - Here, we set all entries for a particular row at once.
740: ! - We can set matrix entries either using either
741: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
742: ! - Note that MatSetValues() uses 0-based row and column numbers
743: ! in Fortran as well as in C.
745: do 20 j=user%ys,user%ye
746: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
747: do 10 i=user%xs,user%xe
748: row = row + 1
749: ! boundary points
750: if (i .eq. 1 .or. j .eq. 1 &
751: & .or. i .eq. user%mx .or. j .eq. user%my) then
752: col(1) = row
753: v(1) = one
754: call MatSetValuesLocal(jac,1,row,1,col,v, &
755: & INSERT_VALUES,ierr)
756: ! interior grid points
757: else
758: v(1) = -hxdhy
759: v(2) = -hydhx
760: v(3) = two*(hydhx + hxdhy) &
761: & - sc*user%lambda*exp(x(i,j))
762: v(4) = -hydhx
763: v(5) = -hxdhy
764: col(1) = row - user%gxm
765: col(2) = row - 1
766: col(3) = row
767: col(4) = row + 1
768: col(5) = row + user%gxm
769: call MatSetValuesLocal(jac,1,row,5,col,v, &
770: & INSERT_VALUES,ierr)
771: endif
772: 10 continue
773: 20 continue
775: return
776: end